diff --git a/doc/opengl-support.dox b/doc/opengl-support.dox
index 7a2b1347b..cad12726b 100644
--- a/doc/opengl-support.dox
+++ b/doc/opengl-support.dox
@@ -454,7 +454,7 @@ Extension                                   | Status
 @m_class{m-doc-external} [ANGLE_base_vertex_base_instance](https://chromium.googlesource.com/angle/angle/+/master/extensions/ANGLE_base_vertex_base_instance.txt) (unlisted) | done
 @m_class{m-doc-external} [ANGLE_provoking_vertex](https://chromium.googlesource.com/angle/angle/+/main/extensions/ANGLE_provoking_vertex.txt) (unlisted) | done
 @m_class{m-doc-external} [ANGLE_polygon_mode](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_polygon_mode.txt) (unlisted) | done
-@m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt) (unlisted) | |
+@m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt) (unlisted) | done
 @gl_extension{APPLE,texture_format_BGRA8888} | done
 @gl_extension{APPLE,clip_distance}          | done
 @gl_extension{ARM,shader_framebuffer_fetch} | missing renderer setup and limit query
@@ -597,7 +597,7 @@ Extension                                   | Status
 @webgl_extension{WEBGL,provoking_vertex}    | missing support in Emscripten
 @webgl_extension{WEBGL,polygon_mode}        | missing support in Emscripten
 @webgl_extension{WEBGL,blend_func_extended} | |
-@webgl_extension{WEBGL,stencil_texturing}   | |
+@webgl_extension{WEBGL,stencil_texturing}   | done
 
 @section opengl-unsupported Unsupported OpenGL features
 
diff --git a/src/Magnum/GL/AbstractTexture.cpp b/src/Magnum/GL/AbstractTexture.cpp
index 90d0ef6ff..bdd0b0390 100644
--- a/src/Magnum/GL/AbstractTexture.cpp
+++ b/src/Magnum/GL/AbstractTexture.cpp
@@ -498,9 +498,15 @@ void AbstractTexture::setCompareFunction(const SamplerCompareFunction function)
 }
 #endif
 
-#if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+#ifndef MAGNUM_TARGET_GLES2
 void AbstractTexture::setDepthStencilMode(const SamplerDepthStencilMode mode) {
-    Context::current().state().texture.parameteriImplementation(*this, GL_DEPTH_STENCIL_TEXTURE_MODE, GLenum(mode));
+    Context::current().state().texture.parameteriImplementation(*this,
+        #ifndef MAGNUM_TARGET_WEBGL
+        GL_DEPTH_STENCIL_TEXTURE_MODE
+        #else
+        GL_DEPTH_STENCIL_TEXTURE_MODE_ANGLE
+        #endif
+        , GLenum(mode));
 }
 #endif
 
diff --git a/src/Magnum/GL/AbstractTexture.h b/src/Magnum/GL/AbstractTexture.h
index 3b30a4076..2c160fe32 100644
--- a/src/Magnum/GL/AbstractTexture.h
+++ b/src/Magnum/GL/AbstractTexture.h
@@ -488,7 +488,7 @@ class MAGNUM_GL_EXPORT AbstractTexture: public AbstractObject {
         void setCompareMode(SamplerCompareMode mode);
         void setCompareFunction(SamplerCompareFunction function);
         #endif
-        #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+        #ifndef MAGNUM_TARGET_GLES2
         void setDepthStencilMode(SamplerDepthStencilMode mode);
         #endif
         #if !(defined(MAGNUM_TARGET_GLES2) && defined(MAGNUM_TARGET_WEBGL))
diff --git a/src/Magnum/GL/CubeMapTexture.h b/src/Magnum/GL/CubeMapTexture.h
index 3f270ca10..a8e980908 100644
--- a/src/Magnum/GL/CubeMapTexture.h
+++ b/src/Magnum/GL/CubeMapTexture.h
@@ -541,16 +541,17 @@ class MAGNUM_GL_EXPORT CubeMapTexture: public AbstractTexture {
         }
         #endif
 
-        #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+        #ifndef MAGNUM_TARGET_GLES2
         /**
          * @brief @copybrief Texture::setDepthStencilMode()
          * @return Reference to self (for method chaining)
          *
          * See @ref Texture::setDepthStencilMode() for more information.
          * @requires_gl43 Extension @gl_extension{ARB,stencil_texturing}
-         * @requires_gles31 Stencil texturing is not available in OpenGL ES 3.0
-         *      and older.
-         * @requires_gles Stencil texturing is not available in WebGL.
+         * @requires_gles31 Extension @m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt)
+         *      in OpenGL ES 3.0.
+         * @requires_webgl_extension WebGL 2.0 and extension
+         *      @webgl_extension{WEBGL,stencil_texturing}
          */
         CubeMapTexture& setDepthStencilMode(SamplerDepthStencilMode mode) {
             AbstractTexture::setDepthStencilMode(mode);
diff --git a/src/Magnum/GL/GL.h b/src/Magnum/GL/GL.h
index f2900fd9a..6f3014edf 100644
--- a/src/Magnum/GL/GL.h
+++ b/src/Magnum/GL/GL.h
@@ -150,7 +150,7 @@ enum class SamplerCompareMode: GLenum;
 #if !(defined(MAGNUM_TARGET_WEBGL) && defined(MAGNUM_TARGET_GLES2))
 enum class SamplerCompareFunction: GLenum;
 #endif
-#if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+#ifndef MAGNUM_TARGET_GLES2
 enum class SamplerDepthStencilMode: GLenum;
 #endif
 
diff --git a/src/Magnum/GL/Sampler.cpp b/src/Magnum/GL/Sampler.cpp
index e20fcaa29..e1da4e3e0 100644
--- a/src/Magnum/GL/Sampler.cpp
+++ b/src/Magnum/GL/Sampler.cpp
@@ -219,7 +219,7 @@ Debug& operator<<(Debug& debug, const SamplerCompareFunction value) {
 }
 #endif
 
-#ifndef MAGNUM_TARGET_GLES
+#ifndef MAGNUM_TARGET_GLES2
 Debug& operator<<(Debug& debug, const SamplerDepthStencilMode value) {
     debug << "GL::SamplerDepthStencilMode" << Debug::nospace;
 
diff --git a/src/Magnum/GL/Sampler.h b/src/Magnum/GL/Sampler.h
index 0d0bbf332..59d6797fc 100644
--- a/src/Magnum/GL/Sampler.h
+++ b/src/Magnum/GL/Sampler.h
@@ -303,23 +303,28 @@ enum class SamplerCompareFunction: GLenum {
 MAGNUM_GL_EXPORT Debug& operator<<(Debug& debug, SamplerCompareFunction value);
 #endif
 
-#if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+#ifndef MAGNUM_TARGET_GLES2
 /**
 @brief Texture sampler depth/stencil mode
 
 @see @ref Texture::setDepthStencilMode() "*Texture::setDepthStencilMode()"
 @m_enum_values_as_keywords
 @requires_gl43 Extension @gl_extension{ARB,stencil_texturing}
-@requires_gles31 Stencil texturing is not available in OpenGL ES 3.0
-    and older.
-@requires_gles Stencil texturing is not available in WebGL.
+@requires_gles31 Extension @m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt)
+    in OpenGL ES 3.0.
+@requires_webgl_extension WebGL 2.0 and extension
+    @webgl_extension{WEBGL,stencil_texturing}
 */
 enum class SamplerDepthStencilMode: GLenum {
     /** Sample depth component */
     DepthComponent = GL_DEPTH_COMPONENT,
 
     /** Sample stencil index (as unsigned integer texture) */
+    #ifndef MAGNUM_TARGET_WEBGL
     StencilIndex = GL_STENCIL_INDEX
+    #else
+    StencilIndex = GL_STENCIL_INDEX_ANGLE
+    #endif
 };
 
 /** @debugoperatorenum{SamplerDepthStencilMode} */
diff --git a/src/Magnum/GL/Test/CubeMapTextureGLTest.cpp b/src/Magnum/GL/Test/CubeMapTextureGLTest.cpp
index cb8e35bf5..96f49ce12 100644
--- a/src/Magnum/GL/Test/CubeMapTextureGLTest.cpp
+++ b/src/Magnum/GL/Test/CubeMapTextureGLTest.cpp
@@ -82,6 +82,8 @@ struct CubeMapTextureGLTest: OpenGLTester {
     #endif
     #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
     void samplingBorderInteger();
+    #endif
+    #ifndef MAGNUM_TARGET_GLES2
     void samplingDepthStencilMode();
     #endif
     #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_WEBGL)
@@ -351,6 +353,8 @@ CubeMapTextureGLTest::CubeMapTextureGLTest() {
               #endif
               #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
               &CubeMapTextureGLTest::samplingBorderInteger,
+              #endif
+              #ifndef MAGNUM_TARGET_GLES2
               &CubeMapTextureGLTest::samplingDepthStencilMode,
               #endif
               #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_WEBGL)
@@ -688,14 +692,19 @@ void CubeMapTextureGLTest::samplingBorderInteger() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 }
+#endif
 
+#ifndef MAGNUM_TARGET_GLES2
 void CubeMapTextureGLTest::samplingDepthStencilMode() {
     #ifndef MAGNUM_TARGET_GLES
     if(!Context::current().isExtensionSupported<Extensions::ARB::stencil_texturing>())
         CORRADE_SKIP(Extensions::ARB::stencil_texturing::string() << "is not supported.");
+    #elif !defined(MAGNUM_TARGET_WEBGL)
+    if(!Context::current().isVersionSupported(Version::GLES310) && !Context::current().isExtensionSupported<Extensions::ANGLE::stencil_texturing>())
+        CORRADE_SKIP("Neither OpenGL ES 3.1 nor" << Extensions::ANGLE::stencil_texturing::string() << "is supported.");
     #else
-    if(!Context::current().isVersionSupported(Version::GLES310))
-        CORRADE_SKIP("OpenGL ES 3.1 not supported.");
+    if(!Context::current().isExtensionSupported<Extensions::WEBGL::stencil_texturing>())
+        CORRADE_SKIP(Extensions::WEBGL::stencil_texturing::string() << "is not supported.");
     #endif
 
     CubeMapTexture texture;
diff --git a/src/Magnum/GL/Test/TextureArrayGLTest.cpp b/src/Magnum/GL/Test/TextureArrayGLTest.cpp
index ae0b60bfd..46808de88 100644
--- a/src/Magnum/GL/Test/TextureArrayGLTest.cpp
+++ b/src/Magnum/GL/Test/TextureArrayGLTest.cpp
@@ -112,9 +112,7 @@ struct TextureArrayGLTest: OpenGLTester {
     #ifndef MAGNUM_TARGET_GLES
     void samplingDepthStencilMode1D();
     #endif
-    #ifndef MAGNUM_TARGET_WEBGL
     void samplingDepthStencilMode2D();
-    #endif
     #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_WEBGL)
     void samplingBorder2D();
     #endif
@@ -356,9 +354,7 @@ TextureArrayGLTest::TextureArrayGLTest() {
         #ifndef MAGNUM_TARGET_GLES
         &TextureArrayGLTest::samplingDepthStencilMode1D,
         #endif
-        #ifndef MAGNUM_TARGET_WEBGL
         &TextureArrayGLTest::samplingDepthStencilMode2D,
-        #endif
         #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_WEBGL)
         &TextureArrayGLTest::samplingBorder2D,
         #endif
@@ -879,16 +875,18 @@ void TextureArrayGLTest::samplingBorderInteger2D() {
 }
 #endif
 
-#ifndef MAGNUM_TARGET_WEBGL
 void TextureArrayGLTest::samplingDepthStencilMode2D() {
     #ifndef MAGNUM_TARGET_GLES
     if(!Context::current().isExtensionSupported<Extensions::EXT::texture_array>())
         CORRADE_SKIP(Extensions::EXT::texture_array::string() << "is not supported.");
     if(!Context::current().isExtensionSupported<Extensions::ARB::stencil_texturing>())
         CORRADE_SKIP(Extensions::ARB::stencil_texturing::string() << "is not supported.");
+    #elif !defined(MAGNUM_TARGET_WEBGL)
+    if(!Context::current().isVersionSupported(Version::GLES310) && !Context::current().isExtensionSupported<Extensions::ANGLE::stencil_texturing>())
+        CORRADE_SKIP("Neither OpenGL ES 3.1 nor" << Extensions::ANGLE::stencil_texturing::string() << "is supported.");
     #else
-    if(!Context::current().isVersionSupported(Version::GLES310))
-        CORRADE_SKIP("OpenGL ES 3.1 is not supported.");
+    if(!Context::current().isExtensionSupported<Extensions::WEBGL::stencil_texturing>())
+        CORRADE_SKIP(Extensions::WEBGL::stencil_texturing::string() << "is not supported.");
     #endif
 
     Texture2DArray texture;
@@ -896,7 +894,6 @@ void TextureArrayGLTest::samplingDepthStencilMode2D() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 }
-#endif
 
 #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_WEBGL)
 void TextureArrayGLTest::samplingBorder2D() {
diff --git a/src/Magnum/GL/Test/TextureGLTest.cpp b/src/Magnum/GL/Test/TextureGLTest.cpp
index 881e5e950..bf6368975 100644
--- a/src/Magnum/GL/Test/TextureGLTest.cpp
+++ b/src/Magnum/GL/Test/TextureGLTest.cpp
@@ -140,7 +140,7 @@ struct TextureGLTest: OpenGLTester {
     #ifndef MAGNUM_TARGET_GLES
     void samplingDepthStencilMode1D();
     #endif
-    #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+    #ifndef MAGNUM_TARGET_GLES2
     void samplingDepthStencilMode2D();
     void samplingDepthStencilMode3D();
     #endif
@@ -542,7 +542,7 @@ TextureGLTest::TextureGLTest() {
         #ifndef MAGNUM_TARGET_GLES
         &TextureGLTest::samplingDepthStencilMode1D,
         #endif
-        #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+        #ifndef MAGNUM_TARGET_GLES2
         &TextureGLTest::samplingDepthStencilMode2D,
         &TextureGLTest::samplingDepthStencilMode3D,
         #endif
@@ -1197,14 +1197,19 @@ void TextureGLTest::samplingBorderInteger2D() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 }
+#endif
 
+#ifndef MAGNUM_TARGET_GLES2
 void TextureGLTest::samplingDepthStencilMode2D() {
     #ifndef MAGNUM_TARGET_GLES
     if(!Context::current().isExtensionSupported<Extensions::ARB::stencil_texturing>())
         CORRADE_SKIP(Extensions::ARB::stencil_texturing::string() << "is not supported.");
+    #elif !defined(MAGNUM_TARGET_WEBGL)
+    if(!Context::current().isVersionSupported(Version::GLES310) && !Context::current().isExtensionSupported<Extensions::ANGLE::stencil_texturing>())
+        CORRADE_SKIP("Neither OpenGL ES 3.1 nor" << Extensions::ANGLE::stencil_texturing::string() << "is supported.");
     #else
-    if(!Context::current().isVersionSupported(Version::GLES310))
-        CORRADE_SKIP("OpenGL ES 3.1 is not supported.");
+    if(!Context::current().isExtensionSupported<Extensions::WEBGL::stencil_texturing>())
+        CORRADE_SKIP(Extensions::WEBGL::stencil_texturing::string() << "is not supported.");
     #endif
 
     Texture2D texture;
@@ -1326,14 +1331,19 @@ void TextureGLTest::samplingBorderInteger3D() {
 
     MAGNUM_VERIFY_NO_GL_ERROR();
 }
+#endif
 
+#ifndef MAGNUM_TARGET_GLES2
 void TextureGLTest::samplingDepthStencilMode3D() {
     #ifndef MAGNUM_TARGET_GLES
     if(!Context::current().isExtensionSupported<Extensions::ARB::stencil_texturing>())
         CORRADE_SKIP(Extensions::ARB::stencil_texturing::string() << "is not supported.");
+    #elif !defined(MAGNUM_TARGET_WEBGL)
+    if(!Context::current().isVersionSupported(Version::GLES310) && !Context::current().isExtensionSupported<Extensions::ANGLE::stencil_texturing>())
+        CORRADE_SKIP("Neither OpenGL ES 3.1 nor" << Extensions::ANGLE::stencil_texturing::string() << "is supported.");
     #else
-    if(!Context::current().isVersionSupported(Version::GLES310))
-        CORRADE_SKIP("OpenGL ES 3.1 is not supported.");
+    if(!Context::current().isExtensionSupported<Extensions::WEBGL::stencil_texturing>())
+        CORRADE_SKIP(Extensions::WEBGL::stencil_texturing::string() << "is not supported.");
     #endif
 
     Texture3D texture;
diff --git a/src/Magnum/GL/Texture.h b/src/Magnum/GL/Texture.h
index 01c5bba5e..66efdc30d 100644
--- a/src/Magnum/GL/Texture.h
+++ b/src/Magnum/GL/Texture.h
@@ -771,7 +771,7 @@ Texture: public AbstractTexture {
         }
         #endif
 
-        #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+        #ifndef MAGNUM_TARGET_GLES2
         /**
          * @brief Set depth/stencil texture mode
          * @return Reference to self (for method chaining)
@@ -786,9 +786,10 @@ Texture: public AbstractTexture {
          *      eventually @fn_gl{ActiveTexture}, @fn_gl{BindTexture} and
          *      @fn_gl_keyword{TexParameter} with @def_gl_keyword{DEPTH_STENCIL_TEXTURE_MODE}
          * @requires_gl43 Extension @gl_extension{ARB,stencil_texturing}
-         * @requires_gles31 Stencil texturing is not available in OpenGL ES 3.0
-         *      and older.
-         * @requires_gles Stencil texturing is not available in WebGL.
+         * @requires_gles31 Extension @m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt)
+         *      in OpenGL ES 3.0.
+         * @requires_webgl_extension WebGL 2.0 and extension
+         *      @webgl_extension{WEBGL,stencil_texturing}
          */
         Texture<dimensions>& setDepthStencilMode(SamplerDepthStencilMode mode) {
             AbstractTexture::setDepthStencilMode(mode);
diff --git a/src/Magnum/GL/TextureArray.h b/src/Magnum/GL/TextureArray.h
index b095dc92d..944fc76c4 100644
--- a/src/Magnum/GL/TextureArray.h
+++ b/src/Magnum/GL/TextureArray.h
@@ -558,22 +558,21 @@ TextureArray: public AbstractTexture {
             return *this;
         }
 
-        #ifndef MAGNUM_TARGET_WEBGL
         /**
          * @brief @copybrief Texture::setDepthStencilMode()
          * @return Reference to self (for method chaining)
          *
          * See @ref Texture::setDepthStencilMode() for more information.
          * @requires_gl43 Extension @gl_extension{ARB,stencil_texturing}
-         * @requires_gles31 Stencil texturing is not available in OpenGL ES 3.0
-         *      and older.
-         * @requires_gles Stencil texturing is not available in WebGL.
+         * @requires_gles31 Extension @m_class{m-doc-external} [ANGLE_stencil_texturing](https://chromium.googlesource.com/angle/angle/+/HEAD/extensions/ANGLE_stencil_texturing.txt)
+         *      in OpenGL ES 3.0.
+         * @requires_webgl_extension WebGL 2.0 and extension
+         *      @webgl_extension{WEBGL,stencil_texturing}
          */
         TextureArray<dimensions>& setDepthStencilMode(SamplerDepthStencilMode mode) {
             AbstractTexture::setDepthStencilMode(mode);
             return *this;
         }
-        #endif
 
         /**
          * @brief @copybrief Texture::setStorage()